(3n-6)(5n+3)=0

Solution for (3n-6)(5n+3)=0 equation:

(3n-6)(5n+3)=0

We multiply parentheses ..

(+15n^2+9n-30n-18)=0

We get rid of parentheses

15n^2+9n-30n-18=0

We add all the numbers together, and all the variables

15n^2-21n-18=0

a = 15; b = -21; c = -18;
Δ = b2-4ac
Δ = -212-4·15·(-18)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-39}{2*15}=\frac{-18}{30}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+39}{2*15}=\frac{60}{30}
=2
$